Problem: Rewrite as a simplified fraction. ${0.\overline{45} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 45.4545...\\ 1x &= 0.4545...\end{align*}}$ Subtracting the two equations, we have: ${99x = 45}$ ${x = \dfrac{45}{99}} $ ${x = \dfrac{5}{11}} $